Here, it should be mentioned that the rectangular central moment LB formulation, while better than its raw moment counterpart, has a reduced stability range when compared to the square lattice based central moment LBM (see e.g., [1]}). This is due to the fact that while the correction terms eliminate the truncation errors arising from the use of the rectangular lattice in the second order moments and recover the desired viscous stress tensor and hence the Navier-Stokes equations, the effects of grid anisotropy and the associated non-GI terms remain in the higher order (kinetic) moments that influence such numerical behavior. However, this stability reduction can be compensated for by the flexibility available in the rectangular LBM in choosing the grid sizes that reflect the nature of the flow being resolved, such as in inhomogeneous shear flows, which then would result in significant improvements in computational efficiency as demonstrated in Sec. REF . The key aspect in such cases is the careful selection of the grid aspect ratio in the range that maintains numerical stability while delivering reductions in the overall computational cost, which depends on the type of flow problem to be simulated. We believe that further improvements are possible by the development of a multiblock rectangular central moment LBM, where instead of resolving the entire domain using a single grid aspect ratio with a relatively low value, appropriate grid aspect ratios can be utilized in few selected zones of the flow domain in such a way that the multiblock interfaces are constrained to match the hydrodynamics from the respective zones. The construction of such general forms of rectangular lattice based LBM will be addressed in a future work.
